Question

graph the image of kite abcd after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated with a scale - factor $k$ centered at the origin, the new point $(x',y')$ is given by $(x',y')=(kx,ky)$.

Step2: Identify the coordinates of the kite vertices

The vertices of kite $ABCD$ are $A(0, - 2)$, $B(2,0)$, $C(0,2)$, $D(-2,0)$.

Step3: Apply the dilation formula

For point $A(0,-2)$:
$x = 0,y=-2,k = 5$, then $x'=5\times0 = 0,y'=5\times(-2)=-10$. So the new point $A'$ is $(0,-10)$.
For point $B(2,0)$:
$x = 2,y = 0,k = 5$, then $x'=5\times2=10,y'=5\times0 = 0$. So the new point $B'$ is $(10,0)$.
For point $C(0,2)$:
$x = 0,y = 2,k = 5$, then $x'=5\times0=0,y'=5\times2 = 10$. So the new point $C'$ is $(0,10)$.
For point $D(-2,0)$:
$x=-2,y = 0,k = 5$, then $x'=5\times(-2)=-10,y'=5\times0 = 0$. So the new point $D'$ is $(-10,0)$.

Step4: Graph the new kite

Plot the points $A'(0,-10)$, $B'(10,0)$, $C'(0,10)$, $D'(-10,0)$ and connect them to form the dilated kite.

Answer:

Graph the kite with vertices $A'(0,-10)$, $B'(10,0)$, $C'(0,10)$, $D'(-10,0)$.